Causal Inference: An Application on Pensioner Poverty

Darwin Del Castillo

07/10/2025

What is poverty?

  • People experience poverty when their resources are not enough to meet their basic needs, such as food, shelter, clothing, and healthcare.
  • It is estimated than as of 2025, ~1.7 million people are living in relative poverty in the UK (1 in 5 pensioners, 17%)1.

Definitions of poverty in the UK2

  • Relative low income: People living in households with income below 60% of the median in that year.
  • Absolute low income: People living in households with income below 60% of the median in 2010/11, adjusted for inflation.

How we measure poverty?

Poverty is a multidimensional concept that goes beyond income and includes social, economic, and psychological aspects.

Why study pensioner health?

Older population is increasing worldwide along with associated burden of disease, particularly NCDs3.

Burden of disease in older adults in UK4

The problem

How to estimate the causal effect of pensioner poverty on health outcomes?

Why measure it?

  • Socioeconomic conditions have been shown to be strong predictors of health outcomes5.
  • There is evidence that income has an impact on health outcomes6,7.
  • These estimates could be used to estimate the impact of social policies on health outcomes through simulations.

Conditions for causal inference on observational studies8

  • Consistency: the values of treatment under comparison correspond to well-defined interventions.

\[A_i = a \Rightarrow Y_i^a = Y_i^A = Y_i\]

  • Exchangeability: the conditional probability of receiving every value of treatment depends only on measured covariates.

\[Y^a \perp\!\!\!\perp A \; \forall a\]

  • Positivity: every subject has a non-zero probability of receiving every value of treatment.

\[\Pr[A = a | L = l] > 0 \; \forall l : \Pr[L = l] \neq 0\]

Challenges

  • Confounding: Many variables are time-varying and affected by prior exposures.
  • Administrative data: Reliance on only administrative data may not capture all relevant confounders.
  • Definition of income9: High heterogeneity in the definition of income (e.g. individual versus household level).
  • Definition of the causal contrast10: What we are comparing, i.e. which point of time? what measure of change?.
  • SUTVA: One household member’s poverty status may affect other members’ health outcomes.
  • Reverse causation: Poor health may lead to poverty due to increased medical expenses or reduced earning capacity.
  • Treatment confounder feedback

Different definitions of income11

Treatment confounder feedback

Poverty and employment status may influence each other over time.

Potential methods for handling these challenges

Marginal Structural Models (MSMs):

  • Models the causal parameter (treatment) directly
  • Appropriate for time-varying exposures with treatment-confounder feedback
  • Susceptible to extreme weights and wide confidence intervals

g-estimation of SNMs:

  • Fits a structural nested model to estimate treatment effect over levels of covariates \(L\)
  • Can model time-varying effect modification12
  • Computationally intensive and requires correct model specification

Doubly Robust Estimation:

  • Combines strengths of both approaches
  • Protection against misspecification
  • More complex implementation

An ideal approach

  1. Define the research question and causal contrast clearly.
  2. Define my estimand13: average treatment effect (ATE), heterogeneous treatment effect (HTE), etc.
  3. Identify and measure as many relevant confounders as possible.
  4. Choose an appropriate method (e.g. MSMs, doubly robust estimation, SNMs) based on the definition of income.
  5. Link administrative data with EHR data to capture health outcomes.
  6. Conduct sensitivity analyses to assess the robustness of findings: comparing two model specifications.
  7. Exploring exogenous sources of variability (e.g. policy changes, governmental transfers, changes in age of retirement).

References

1.
Centre for Ageing Better. State of ageing 2025 [Internet]. London, England: Centre for Ageing Better; 2025. Available from: https://ageing-better.org.uk/financial-security-state-ageing-2025
2.
Francis-Devine B. Poverty in the UK: statistics [Internet]. House of Commons Library; 2025. Report No.: SN07096. Available from: https://commonslibrary.parliament.uk/research-briefings/sn07096/
3.
GBD 2021 Diseases and Injuries Collaborators. Global incidence, prevalence, years lived with disability (YLDs), disability-adjusted life-years (DALYs), and healthy life expectancy (HALE) for 371 diseases and injuries in 204 countries and territories and 811 subnational locations, 1990-2021: A systematic analysis for the global burden of disease study 2021. Lancet. 2024 May 18;403:2133–61.
4.
Chen QF, Ni C, Jiang Y, Chen L, Liao H, Gao J, et al. Global burden of disease and its risk factors for adults aged 70 and older across 204 countries and territories: A comprehensive analysis of the global burden of disease study 2021. BMC Geriatr. 2025 Jul 2;25:462.
5.
Marmot M. Social determinants of health inequalities. Lancet. 2005;365:1099–104.
6.
Gunasekara FI, Carter K, Blakely T. Change in income and change in self-rated health: Systematic review of studies using repeated measures to control for confounding bias. Soc Sci Med. 2011 Jan;72:193–201.
7.
Cooper K, Stewart K. Does household income affect children’s outcomes? A systematic review of the evidence. Child Indic Res. 2021 Jun;14:981–1005.
8.
Hernán MA, Robins JM. Causal inference: What if. 3rd ed. Boca Raton, FL: CRC Press; 2025.
9.
Shi J, Tarkiainen L, Martikainen P, Raalte A van. The impact of income definitions on mortality inequalities. SSM Popul Health. 2021 Sep;15:100915.
10.
Igelström E, Craig P, Lewsey J, Lynch J, Pearce A, Katikireddi SV. Causal inference and effect estimation using observational data. J Epidemiol Community Health. 2022 Nov;76:960–6.
11.
Igelström E, Kopasker D, Craig P, Lewsey J, Katikireddi SV. Estimating the causal effects of income on health: How researchers’ definitions of "income" matter. BMC Public Health. 2024 Jun 11;24:1572.
12.
Robins JM, Hernán MA, Rotnitzky A. Effect modification by time-varying covariates. Am J Epidemiol. 2007 Nov 1;166:994-1002; discussion 1003-4.
13.
Lundberg I, Johnson R, Stewart BM. What is your estimand? Defining the target quantity connects statistical evidence to theory. Am Sociol Rev. 2021 Jun;86:532–65.